Analytical representations for simple and composite polytropes and their moments of inertia

作者：Criss Robert E; Hofmeister Anne M^*

来源：New Astronomy, 2015, 36: 26-31.

DOI：10.1016/j.newast.2014.09.012

• Analytical methods
• Polytropes
• Exoplanets

Polytropes are widely applied in astrophysics. To facilitate their use, we derive analytical formulae for the moment of inertia as a function of polytropic index. We also provide 1- and 3-parameter equations that replicate the density variations in polytropic bodies to varying degrees of accuracy, determined by numerical calculations and analytical results for polytropic indices between 0 and 5. As an example, we construct a composite polytrope, suitable for gas giants, exoplanets, or tiny sub-solar dwarfs, wherein an inner sphere is modeled by constant density, which represents the density jump associated with production of a relatively incompressible solid, and an outer envelope is modeled as having a polytropic index near 2.5, which corresponds to a diatomic gas. Envelope sizes are constrained by the moment of inertia.

• 出版日期2015-4